The OTOCs are defined as the average of the squared commutator, i.e., \(C(t)=-\langle [A(t),B]^2\rangle \) , where both operators \(A(t)=U^{\dagger }(t)AU(t)\)  and \(B\)  are evaluated in the Heisenberg picture, and the \(\langle \cdots \rangle =\langle \psi (t_0)|\cdots |\psi (t_0)\rangle \)  indicates the expectation value taken over the initial state \(|\psi (t_0)\rangle \)  [1]}. It usually uses the thermal states for taking the average in investigation of OTOCs of lattice systems. For the Floquet-driven system, however, there is no the well-defined thermal states, as the temperature trends to be infinity as time evolves [2]}. Without loss of generality, we choose a Gaussian wavepacket as an initial state, i.e., \(\psi {(\theta ,0)}=(\sigma /\pi )^{1/4} \exp (-\sigma \theta ^{2}/2)\)  with \(\sigma =10\) . We consider the case with \(A=\theta \)  and \(B=p^{m}\)  (\(m\in \mathbb {N}\) ), hence \(C(t)=-\langle [\theta (t_{}),p^{m}]^2\rangle \) .
